An ac source of angular frequency \(\omega\) is fed across a resistor \(r\) and a capacitor \(C\) in series. \(I\) is the current in the circuit. If the frequency of the source is changed to \(\frac{\omega}{3}\) (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency \(\omega\).
1. | \(\sqrt{\dfrac{3}{5}}\) | 2. | \(\sqrt{\dfrac{2}{5}}\) |
3. | \(\sqrt{\dfrac{1}{5}}\) | 4. | \(\sqrt{\dfrac{4}{5}}\) |
1. | \(\frac{\sqrt{5} R}{2} ,\tan^{- 1} \left(2\right)\) | 2. | \(\frac{\sqrt{5} R}{2} , \tan^{- 1} \left(\frac{1}{2}\right)\) |
3. | \(\sqrt{5} X_{C} ,\tan^{- 1} \left(2\right)\) | 4. | \(\sqrt{5} R , \tan^{- 1} \left(\frac{1}{2}\right)\) |
In a series \(LCR\) circuit, which one of the following curves represents the variation of impedance \((Z)\) with frequency \((f)\)?
1. | ![]() |
2. | ![]() |
3. | ![]() |
4. | ![]() |
The variation of the instantaneous current \((I)\) and the instantaneous emf \((E)\) in a circuit are shown in the figure. Which of the following statements is correct?
1. | The voltage lags behind the current by \(\frac{\pi}{2}\). |
2. | The voltage leads the current by \(\frac{\pi}{2}\). |
3. | The voltage and the current are in phase. |
4. | The voltage leads the current by \(\pi\). |
A constant voltage at different frequencies is applied across a capacitance \(C\) as shown in the figure.
Which of the following graphs accurately illustrates how current varies with frequency?
1. | ![]() |
2. | ![]() |
3. | ![]() |
4. | ![]() |
The output current versus time curve of a rectifier is shown in the figure.
The average value of the output current in this case will be:
1. | \(0\) | 2. | \(I_0 \over 2\) |
3. | \(2I_0 \over \pi\) | 4. | \(I_0\) |
When an AC source of emf \(e = E_0 \sin (100t)\) is connected across a circuit, the phase difference between the emf \(e\) and the current \(i\) in the circuit is observed to be \(\frac{\pi}{4}\) as shown in the diagram. If the circuit consists only of \(RC\) or \(LC\) in series, then what is the relationship between the two elements?
1. | \(R=1~\text{k} \Omega, C=10 ~\mu \text{F}\) |
2. | \(R=1~\text{k}\Omega, C=1~\mu \text{F}\) |
3. | \(R=1 ~\text{k}\Omega, L=10 ~\text{H}\) |
4. | \(R=1 ~\text{k}\Omega, L=1~\text{H}\) |
In the diagram, two sinusoidal voltages of the same frequency are shown. What is the frequency and the phase relationship between the voltages?
Frequency in Hz | Phase lead of \(N\) over \(M\) in radians | |
1. | \(0.4\) | \(-\pi/4\) |
2. | \(2.5\) | \(-\pi/2\) |
3. | \(2.5\) | \(+\pi/2\) |
4. | \(2.5\) | \(-\pi/4\) |
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)
1. | \(\frac{1}{100}~\text{sec}\) | 2. | \(\frac{1}{200}~\text{sec}\) |
3. | \(\frac{1}{300}~\text{sec}\) | 4. | \(\frac{1}{400}~\text{sec}\) |